The Interplay between Individual and Collective Activity: an Analysis of Classroom Discussions about the Sierpinski Triangle

Abstract This article uses a cultural-developmental framework to illuminate the interplay between collective and individual activity in mathematical reasoning displayed university Masters level lesson on fractals. During whole class small group discussions, eleven students, guided by an instructor, engage inductive about area perimeter of Sierpinski triangle, unique object with zero infinite perimeter. As participants conceptualize communicate problem, they unwittingly generate linguistic register action word forms (e.g., fencing , zooming ) infinity serve Sierpinski-linked functions, that we document first analytic section article. In second section, report developmental analysis microgenetic, ontogenetic, sociogenetic shifts constitutive their varied functions participants’ activities. third provide cultural classroom’s practices, practices enable constrain constructions form-function relations constituting register. We examine ways which work establish common ground talk communicative exchanges, exchanges supported classroom norms for public displays active listening one another’s ideas. show it is as emerges reproduced altered. conclude pointing can be extended learning processes other settings.